I have looked at Yards per Play (YPP) for games where opponents had 7 days to prepare vs. more than 7 days to prepare.
This comparison is only for FBS opponents and we do worse against teams with more preparation. I do not know for sure if this comparison is meaningful or if it is statistically significant data. I have put in all the data in google docs (check out all 3 sheets) and shared it online here:
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The stat I am actually looking at is the ratio of YPP GT got against a team to YPP that team's defense had for the whole season.
In other words the ratio I am looking at:
Ratio=
(YPP GT had in game against team X) /
(YPP team X's defense had all season)
The average of these ratios for 2008-2010:
Teams with 7 or less: 1.15
Teams with more than 7: 1.06
The same analysis done on Yards per Carry Ratio and Yards per Pass Attempt Ratio is as follows:
Teams with 7 or less: 1.37 (YPC) 1.27 (YPPAR)
Teams with more than 7: 1.33 (YPC) 1.03 (YPPAR)
It's also important to know how good the defenses are on average:
Teams with 7 or less: 5.16 yards per play
Teams with more than 7: 5.05 yards per play
The difference in defenses is not big enough to explain the ratios, but still good to know.